   # An iron sphere has a radius of 3.4 cm. How many iron atoms are in the sphere? Iron has a density of 7 .86 g/cm 3 , and a sphere has a volume of V = ( 4 3 ) × π r 3 . ### Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692

#### Solutions

Chapter
Section ### Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692
Chapter 3, Problem 55E
Textbook Problem
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## An iron sphere has a radius of 3.4 cm. How many iron atoms are in the sphere? Iron has a density of 7 .86 g/cm 3 , and a sphere has a volume of V = ( 4 3 ) × π r 3 .

Interpretation Introduction

Interpretation:

The number of iron atoms in the given sphere is to be calculated.

Concept Introduction:

 The volume of the sphere is represented as V=43πr3, where V is the volume and r is the radius.

 A mole is a unit of amount of substance. It relates a number of particles to the molar mass.

 One mole of a substance contains Avogadro’s number, that is, 6.022×1023 particles. The number remains constant regardless of the nature of the substance. One mole of an atom contains 6.022×1023 atoms. One mole of molecules contains 6.022×1023 molecules.

 It also relates to the molar mass of a substance in grams. One mole of a substance weighs that amount in grams, which is equal to its molar mass.

 Density is the ratio of the mass of a substance to its volume.

### Explanation of Solution

Given information:

Radius of sphere 3.4 cmDensity of iron is 7.86 g/cm3

The calculation of the volume of a sphere is as follows:

Volume of sphere = 43πr3

Substitute the values in the above equation:

Volume of sphere = 43×3.14×(3.4 cm)3Volume of sphere = 164.55 cm3

Now, calculate the mass of iron using density as follows:

Density of iron  = Mass of iron in sphereVolume of sphereMass of iron in sphere = Density of iron× Volume of sphere

Substitute the values in the above equation:

mass of iron = 7.86 gcm3× 164

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